public void Compute(OptionPosition option)
{
var t = option.TimeToExpiry.TotalDays / 365.0;
if (Math.Abs(t) < Double.Epsilon)
{
return;
}
var d1 = Math.Log(option.UnderlyingPrice / option.Strike) + (option.InterestRate - option.DividendRate + Math.Pow(option.Volatility, 2)) / t;
var d2 = d1 - option.Volatility * Math.Sqrt(t);
// when calculating option greeks keep in mind that we calculate greek for position,
// and that's why BS formulas for greeks must be multiplied by -1 in case we're selling options
// so formulas for greeks are [sign * BSFormula]
if (option.Type == OptionType.Call)
{
option.OptionPrice = option.UnderlyingPrice * NormalDistribution.Phi(d1) -
option.Strike * Math.Exp(-option.InterestRate * t) * NormalDistribution.Phi(d2);
option.Delta = Math.Exp(-option.DividendRate * t) * NormalDistribution.Phi(d1);
option.Theta = -Math.Exp(-option.DividendRate * t) * option.UnderlyingPrice * NormalDistribution.Density(d1) *
option.Volatility / (2 * Math.Sqrt(t))
+
option.DividendRate * Math.Exp(-option.DividendRate * t) * option.UnderlyingPrice *
NormalDistribution.Phi(d1)
-
option.InterestRate * option.Strike * Math.Exp(-option.InterestRate * t) *
NormalDistribution.Phi(d2);
option.Rho = t * option.Strike * Math.Exp(-option.InterestRate * t) * NormalDistribution.Phi(d2);
}
else
{
option.OptionPrice = -option.UnderlyingPrice * NormalDistribution.Phi(-d1) +
option.Strike * Math.Exp(-option.InterestRate * t) * NormalDistribution.Phi(-d2);
option.Delta = Math.Exp(-option.DividendRate * t) * (NormalDistribution.Phi(d1) - 1);
option.Theta = -Math.Exp(-option.DividendRate * t) * option.UnderlyingPrice * NormalDistribution.Density(d1) *
option.Volatility / (2 * Math.Sqrt(t))
-
option.DividendRate * Math.Exp(-option.DividendRate * t) * option.UnderlyingPrice *
NormalDistribution.Phi(-d1)
+
option.InterestRate * option.Strike * Math.Exp(-option.InterestRate * t) *
NormalDistribution.Phi(-d2);
option.Rho = -t *option.Strike *Math.Exp(-option.InterestRate *t) * NormalDistribution.Phi(-d2);
}
option.Gamma = Math.Exp(-option.DividendRate * t) * NormalDistribution.Density(d1) /
(option.UnderlyingPrice * option.Volatility * Math.Sqrt(t));
option.Vega = Math.Exp(-option.DividendRate * t) * option.UnderlyingPrice * NormalDistribution.Density(d1) *
Math.Sqrt(t);
SideHelper.FixGreeksAccordingToSide(option);
}
public void Compute(OptionPosition option)
{
int steps = option.TreeSteps;
double s = option.UnderlyingPrice;
var t = option.TimeToExpiry.TotalDays / 365.0;
if (Math.Abs(t) < Double.Epsilon)
{
return;
}
if (option.TreeSteps == 0)
{
return;
}
var deltaT = t / (double)steps;
if (deltaT >= Math.Pow(option.Volatility, 2) / Math.Pow(option.InterestRate - option.DividendRate, 2))
{
return;
}
double u = Math.Exp(option.Volatility * Math.Sqrt(t));
double d = 1 / u;
var prices = GetPrices(option.Type == OptionType.Call, option.UnderlyingPrice, t, steps, option.Volatility,
option.Strike, option.InterestRate, option.DividendRate);
// x x x
// x x
// x
option.OptionPrice = prices[0, 0];
option.Delta = (prices[1, 1] - prices[1, 0]) / (s * u - s * d);
option.Gamma = ((prices[2, 2] - prices[2, 1]) / (s * u * u - s * u * d) -
(prices[2, 1] - prices[2, 0]) / (s * u * d - s * d * d)) / (0.5 * (s * u * u - s * d * d));
option.Theta = (prices[2, 1] - prices[0, 0]) / (2 * deltaT);
option.Vega =
(GetPrices(option.Type == OptionType.Call, option.UnderlyingPrice, t, steps, option.Volatility * 1.01,
option.Strike, option.InterestRate, option.DividendRate)[0, 0]
- option.OptionPrice) / (option.Volatility * 0.01);
option.Rho =
(GetPrices(option.Type == OptionType.Call, option.UnderlyingPrice, t, steps, option.Volatility,
option.Strike, option.InterestRate * 1.01, option.DividendRate)[0, 0]
- option.OptionPrice) / (option.InterestRate * 0.01);
SideHelper.FixGreeksAccordingToSide(option);
}
public void Compute(OptionPosition option)
{
var t = option.TimeToExpiry.TotalDays / 365.0;
if (Math.Abs(t) < Double.Epsilon)
{
return;
}
if (option.TreeSteps == 0)
{
return;
}
Func <double, double> getWithTime = x => GetPrice(option.Type == OptionType.Call, option.UnderlyingPrice, option.Strike,
option.Volatility, option.InterestRate, option.DividendRate, x, option.TreeSteps)[0, 0];
Func <double, double> getWithVol = x => GetPrice(option.Type == OptionType.Call, option.UnderlyingPrice, option.Strike,
x, option.InterestRate, option.DividendRate, t, option.TreeSteps)[0, 0];
Func <double, double> getWithR = x => GetPrice(option.Type == OptionType.Call, option.UnderlyingPrice, option.Strike,
option.Volatility, x, option.DividendRate, t, option.TreeSteps)[0, 0];
var deltaT = t / (double)option.TreeSteps;
double u = Math.Exp(option.Volatility * Math.Sqrt(2 * deltaT));
double d = Math.Exp(-option.Volatility * Math.Sqrt(2 * deltaT));
var prices = GetPrice(option.Type == OptionType.Call, option.UnderlyingPrice, option.Strike,
option.Volatility, option.InterestRate, option.DividendRate, t, option.TreeSteps);
option.OptionPrice = prices[0, 0];
option.Delta = (prices[1, 2] - 2 * prices[1, 1] + prices[1, 0]) / (option.UnderlyingPrice * (u - d));
option.Gamma = ((prices[2, 4] - 2 * prices[2, 3] + prices[2, 2]) / (Math.Pow(option.UnderlyingPrice * (u * u - u), 2)) -
(prices[2, 2] - 2 * prices[2, 1] + prices[2, 0]) / (Math.Pow(option.UnderlyingPrice * (d - d * d), 2))) /
(0.5 * (option.UnderlyingPrice * (u * u - d * d)));
option.Theta = (getWithTime(t + deltaT) - getWithTime(t - deltaT)) / (2 * deltaT);
double volDelta = option.Volatility * 0.01;
option.Vega = (getWithVol(option.Volatility + volDelta) - getWithVol(option.Volatility - volDelta)) /
(2 * volDelta);
double rDelta = option.InterestRate * 0.01;
option.Rho = (getWithR(option.InterestRate + rDelta) - getWithR(option.InterestRate - rDelta)) /
(2 * rDelta);
SideHelper.FixGreeksAccordingToSide(option);
}